An axial-azimuthal two-dimensional Hall thruster discharge model was developed for analyzing gradient drift instability (GDI) and cross field electron transport enhancement induced solely by the GDI. A hybrid particle-fluid model was used for the partially ionized plasma, where the inertialess electron fluid in the quasineutral plasma was assumed. A nonoscillatory numerical method was proposed for the potential solver in the electron fluid model to avoid numerical instability and analyze the physics of GDI accurately. A simulation is performed for a 1 kW-class anode-layer-type Hall thruster, and the flow field with plasma instability is presented. Plasma instability with vortex-like structures is observed in the acceleration and plume regions. The generated plasma instability enhances the cross field electron transport in the axial direction around the channel exit and in the plume region. Grid convergence is confirmed regarding the effect of electron transport enhancement, which indicates that cross field electron transport enhancement is based on the plasma instability. Furthermore, the comparison between the simulation results and linear perturbation analyses demonstrates that the simulated plasma instability reflects the theory of GDI. Thus, it is concluded that the hybrid model is useful for the analyses of GDI, and the GDI can enhance the cross field electron transport in Hall thrusters.
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